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GCE MAY 2007 : AS, C1: Core Mathematics 1(Irish Medium)

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ADVANCED SUBSIDIARY (AS) General Certificate of Education 2007 Matamaitic Aonad Meas naithe C1 ag meas n Mod l C1: AS Cro mhatamaitic 1 [AMC11] D LUAIN 21 BEALTAINE, MAIDIN AM 1 uair 30 n im ad. TREOIR D IARRTH IR Scr obh d Uimhir L rionaid agus d Uimhir Iarrth ra ar an Leabhr n Freagra at leis seo. Freagair gach ceann de na hocht gceist. Taispe in go soil ir forbairt ioml n do fhreagra . Ba cheart na freagra a thabhairt ceart go dt 3 fhigi r bhun sacha mura ndeirtear a mhalairt. N l s ceadmhach aon is a s id sa ph ip ar seo le h ireamh a dh anamh. EOLAS D IARRTH IR Is 75 an marc ioml n don ph ip ar seo. L ir onn figi ir idir l ib n ar thaobh na l imhe deise de leathanaigh na marcanna at ag dul do gach ceist n do gach cuid de cheist. T c ip den leabhr n Foirml Matamaitice agus T bla ar f il. AMC1S7 1937.02 Freagair gach ceann de na hocht gceist. Taispe in go soil ir forbairt ioml n do fhreagra . Ba ch ir freagra a thabhairt ceart go dt 3 fhigi r bhun sacha mura ndeirtear a mhalairt. N l s ceadmhach aon is a s id sa ph ip ar seo le h ireamh a dh anamh. 1 (a) Athscr obh an slonn th os agus ainmneoir c imheasta aige 4 7 2 + 7 [3] 2(x2 1) x+1 [3] (b) Simpligh chomh fada agus is f idir 2 (a) Sa l ar id in F or 1 anseo th os taispe ntar an graf den fheidhm y = f( x) F or 1 Ar l ar id leithleacha sceitse il na graif de: (i) y = f( x); [2] (ii) y = f( x 2), [2] ag taispe int go soil ir na point mar a dtrasna onn na graif na haiseanna. AMC1S7 1937.02 2 [Turn over (b) (i) Agus teoirim na bhfacht ir in s id agat, taispe in go bhfuil (x 2) ina fhacht ir de (ii) Uaidh sin facht irigh go hioml n an slonn 2x3 + 3x2 11x 6 [3] (iii) Uaidh sin r itigh an chothrom id 2x3 + 3x2 11x 6 = 0 [3] 3 (i) Sceitse il an cuar ag taispe int go soil ir na point mar a dtrasna onn an cuar na haiseanna. (ii) Faigh cothrom id an tadhla don chuar ag an phointe mar a bhfuil x = 2 AMC1S7 1937.02 2x3 + 3x2 11x 6 [2] y = 6 x x2 [3] y = 6 x x2 3 [6] [Tiontaigh an leathanach 4 N ghlacfar le r iteach ar an cheist seo a gheofar le l ar id de r ir sc la. In F or 2 anseo th os taispe ntar eitleog ABCD. F or 2 Is iad (1, 6) comhordan id pointe B. Is iad (7, 4) comhordan id pointe D. (i) Faigh comhordan id M l rphointe BD. [2] (ii) Faigh f na na l ne BD. [2] (iii) Uaidh sin faigh cothrom id na l ne AC. [3] Is iad (3, a) comhordan id pointe A agus is iad (c, 11) comhordan id pointe C. (iv) Faigh a agus c. AMC1S7 1937.02 [2] 4 [Turn over Is x m adar an fad agus is y m adar an leithead at san url r de bhoth n dronuilleogach mar a thaispe ntar in F or 3 anseo th os. y x F or 3 Is 16 m iml ne url r an bhoth in. (i) Scr obh cothrom id a cheangl idh x agus y Is 38 m an fad at i dtrasn n url r an bhoth in. (iii) Uaidh sin taispe in go bhfuil (iv) Faigh fad agus leithead url r an bhoth in. 6 (i) Tr d an ionad y = 3x a s id athscr obh an slonn i dt arma y (ii) Uaidh sin r itigh an chothrom id (ii) Scr obh cothrom id eile a cheangl idh x agus y AMC1S7 1937.02 x2 8x + 13 = 0 [1] [1] [3] [4] 3(32x) 28(3x) + 9 [2] 3(32x) 28(3x) + 9 = 0 [5] [Tiontaigh an leathanach 7 T coime d n le d anamh faoi choinne liathr id lead ige. Is a bheidh ann sorc ir oscailte agus bonn ciorclach agus cl dach a mbeidh cruth leathsf ir air, mar a thaispe ntar in F or 4 anseo th os. F or 4 4 Toirt = r3 3 Toirt = r2h Achar = 4 r2 Achar dromchla chuair = 2 rh Sf ar Sorc ir Is r cm ga an tsorc ra agus is h cm an airde. Is r cm ga an leathsf ir. 320 Caithfidh toirt de cm3 a bheith sa choime d n. 3 (i) Scr obh h i dt arma r (ii) Uaidh sin taispe in gurb an t-achar dromchla ioml n a bheidh sa choime d n. [4] 5 2 640 1 r + r 3 3 (iii) Faigh an luach de r a fh gfaidh gur osluach achar dromchla ioml n an choime d in. AMC1S7 1937.02 6 [4] [7] [Turn over 8 Is an chothrom id at ag cuar y = 2x2 + 5 Is an chothrom id at ag l ne dh reach y = mx 3 Trasna onn an l ne an cuar ag dh phointe. Faigh raon na luachanna a d fh adfadh a bheith ag m. AMC1S7 1937.02 7 [8] S 1/06 0000 7-005-1 [Turn over

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Additional Info : Gce Mathematics May 2007 Assessment Unit C1 Module C1:Core Mathematics 1 (Irish Medium)
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